In this section we review, and in some cases, re-derive the elementary properties
we shall need about the quadratic forms over \({{\mathbb {Q}}}_p\) , according to dimension
(\(n=3\)  and \(n=4\) ) as well as type of prime (\(p\equiv 1\mod {4}\) , \(p\equiv 3 \mod {4}\) 
and \(p=2\) ). Comprehensive treatments of this material can be found in
the books of Cassels [1]} and Serre [2]}.
